Separation of Church and State actually isn't in the Bill of Rights or the Constitution. It comes from a letter Thomas Jefferson wrote while president to the Danbury, Connecticut Baptist Association in 1802. It became precedent through court cases but it is not written down in either the BoR or Constitution.

The original idea of it was actually to protect the Church from the State, not the State from the Church. The Danbury Baptists were concerned that their state constitution had no explicit guarantees of their religious freedoms and they worried the government might try and establish a national religion. Jefferson wrote the letter to reassure them that it was not something to worry about since the Constitution says that the legislature shall "make no law respecting an establishment of religion, or prohibiting the free exercise thereof". It is this sentence, he said, that served to build a "wall of separation between Church & State".